%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO069-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:06:38 PM UTC 2026
% Result : Unsatisfiable 4.15s 1.22s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 77 ( 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D,E,F,G] : multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,G))),multiply(D,multiply(G,F,E),C)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(a,b,inverse(b)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(a,b,inverse(b)) != a,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : multiply(multiply(X0,X1,X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)) = multiply(X1,multiply(X2,inverse(multiply(X0,X1,X8)),X8),X0),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f12,plain,
! [X0,X1,X2] : X0 = multiply(inverse(X1),multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),X1),
inference(paramodulation,[status(thm)],[f3,f8]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,inverse(X2),X3),inverse(multiply(X2,inverse(X2),X3)),multiply(X2,inverse(X2),X4))),X4) = X1,
inference(paramodulation,[status(thm)],[f12,f3]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),multiply(X5,inverse(multiply(X4,inverse(X4),X6)),X6),multiply(X2,X3,inverse(X4)))),multiply(X3,X5,X2)) = X1,
inference(paramodulation,[status(thm)],[f12,f3]) ).
fof(f382,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0),X1),inverse(X2),multiply(inverse(X3),multiply(X4,inverse(multiply(multiply(X4,X3,X5),multiply(inverse(X3),inverse(multiply(X5,inverse(X5),X6)),X6),multiply(X4,X3,inverse(X5)))),X2),X3)) = X1,
inference(paramodulation,[status(thm)],[f55,f3]) ).
fof(f824,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2)) = X1,
inference(paramodulation,[status(thm)],[f55,f382]) ).
fof(f934,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2)) = multiply(inverse(X5),X1,X5),
inference(paramodulation,[status(thm)],[f824,f824]) ).
fof(f1013,plain,
! [X0,X1] : X0 = multiply(inverse(X1),X0,X1),
inference(forward_demodulation,[status(thm)],[f824,f934]) ).
fof(f1047,plain,
! [X0,X1,X2] : X0 = multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),
inference(backward_demodulation,[status(thm)],[f1013,f12]) ).
fof(f1647,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(X1,inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f1013,f1047]) ).
fof(f1778,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),X3)),X3) = X1,
inference(backward_demodulation,[status(thm)],[f1647,f49]) ).
fof(f1782,plain,
! [X0,X1] : X0 = multiply(X0,inverse(X1),X1),
inference(backward_demodulation,[status(thm)],[f1647,f1047]) ).
fof(f1814,plain,
! [X0,X1,X2] : multiply(multiply(X0,inverse(X0),X1),inverse(X2),X2) = X1,
inference(forward_demodulation,[status(thm)],[f1647,f1778]) ).
fof(f2092,plain,
! [X0,X1] : multiply(X0,inverse(X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1782,f1814]) ).
fof(f2094,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f1013,f2092]) ).
fof(f2466,plain,
! [X0,X1] : X0 = multiply(X0,X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f2094,f1782]) ).
fof(f2468,plain,
a != a,
inference(backward_demodulation,[status(thm)],[f2466,f4]) ).
fof(f2496,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO069-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 % Computer : n005.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 13:52:02 UTC 2026
% 0.19/0.50 % CPUTime :
% 0.19/0.52 % Drodi V4.1.1
% 4.15/1.22 % Refutation found
% 4.15/1.22 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.15/1.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.53/1.28 % Elapsed time: 0.754851 seconds
% 2.53/1.28 % CPU time: 5.623231 seconds
% 2.53/1.28 % Total memory used: 142.433 MB
% 2.53/1.28 % Net memory used: 141.184 MB
%------------------------------------------------------------------------------